CHAPTER III: CONICS AND QUADRICS - OCW UPM
CHAPTER III: CONICS AND QUADRICS - OCW UPM
CHAPTER III: CONICS AND QUADRICS - OCW UPM
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4.1.1 Projective classification<br />
AFFINE <strong>AND</strong> PROJECTIVE GEOMETRY, E. Rosado & S.L. Rueda<br />
1. If det A ≠ 0, then the quadric Q is ordinary or not degenerate.<br />
2. If det A = 0, then the quadric Q is degenerate.<br />
a) If rank(A) = 3, then Q has an unique singular point P .<br />
If P is a proper point, then Q is a cone with vertex P .<br />
If P is an improper point, then Q is a cylinder.<br />
b) If rank(A) = 2, then Q has a line of singular points and Q is a pair of<br />
planes with intersection the line of singular points.<br />
c) If rank(A) = 1, then Q has a plane of singular points and Q is a<br />
double plane.
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